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DRA Systems: OR-Objects 1.2.4: Interface  SVDecompositionI
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  SUMMARY: &nbsp;INNER&nbsp;|&nbsp;FIELD&nbsp;|&nbsp;CONSTR&nbsp;|&nbsp;<A HREF="#method_summary">METHOD</A></FONT></TD>
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drasys.or.linear.algebra</FONT>
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Interface  SVDecompositionI</H2>
<DL>
<DT><B>All Known Implementing Classes:</B> <DD><A HREF="../../../../drasys/or/linear/algebra/QRIteration.html">QRIteration</A></DD>
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<DL>
<DT>public interface <B>SVDecompositionI</B><DT>extends <A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html">DecompositionI</A></DL>

<P>
The interface used by all algorithms to access singular value decomposition algorithms.
<P>
<DL>
<DT><B>See Also: </B><DD><A HREF="../../../../drasys/or/linear/algebra/QRIteration.html"><CODE><P><FONT COLOR="#CC0000"><FONT SIZE=+1>References:</FONT></FONT><FONT SIZE=+1></FONT><P><B><A NAME="0155510053"HREF="http://www.amazon.com/exec/obidos/ISBN=0155510053/opsresearchcomA/" TARGET="amazon.com">Linear Algebra and Its Applications</A></B><BR>&nbsp;&nbsp;&nbsp;&nbsp;Gilbert Strang / Hardcover / Published 1988<BR><B><A NAME="0801854148"HREF="http://www.amazon.com/exec/obidos/ISBN=0801854148/opsresearchcomA/" TARGET="amazon.com">Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences)</A></B><BR>&nbsp;&nbsp;&nbsp;&nbsp;Gene H. Golub, Charles F. Van Loan (Contributor) / Paperback / Published 1996<BR><B><A NAME="0521431085"HREF="http://www.amazon.com/exec/obidos/ISBN=0521431085/opsresearchcomA/" TARGET="amazon.com">Numerical Recipes in C : The Art of Scientific Computing</A></B><BR>&nbsp;&nbsp;&nbsp;&nbsp;William H. Press, et al / Hardcover / Published 1993<BR><B><A NAME="0898712602"HREF="http://www.amazon.com/exec/obidos/ISBN=0898712602/opsresearchcomA/" TARGET="amazon.com">Parallel Algorithms for Matrix Computations </A></B><BR>&nbsp;&nbsp;&nbsp;&nbsp;K.A. Gallivan / Paperback / Published 1990<BR></CODE></A></DL>
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<B>Method Summary</B></FONT></TD>
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<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#computeConditionNumber()">computeConditionNumber</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the condition number of the matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/DenseMatrix.html">DenseMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#computeInverse()">computeInverse</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the inverse of the decomposed matrix from the components.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#computeInverse(drasys.or.matrix.MatrixI)">computeInverse</A></B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the inverse of the decomposed matrix from the components.</TD>
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<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#decompose(drasys.or.matrix.MatrixI)">decompose</A></B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;matrix)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Decompose matrix A into U, W and V matrices.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/DenseMatrix.html">DenseMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#getU()">getU</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the U matrix.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#getU(drasys.or.matrix.MatrixI)">getU</A></B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the U matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/DenseMatrix.html">DenseMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#getV()">getV</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the V matrix.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#getV(drasys.or.matrix.MatrixI)">getV</A></B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the V matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/SparseMatrix.html">SparseMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#getW()">getW</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the W matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#getW(drasys.or.matrix.MatrixI)">getW</A></B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the W matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#isIllConditioned()">isIllConditioned</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns true if the decomposed matrix is ill-conditioned.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#isSingular()">isSingular</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns true if the decomposed matrix is singular.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/DenseVector.html">DenseVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#solveEquations(drasys.or.matrix.VectorI)">solveEquations</A></B>(<A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A>&nbsp;rightHandSides)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Uses backsubstitution to solve the simultaneous equations.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../drasys/or/linear/algebra/SVDecompositionI.html#solveEquations(drasys.or.matrix.VectorI, drasys.or.matrix.VectorI)">solveEquations</A></B>(<A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A>&nbsp;rightHandSides,
               <A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A>&nbsp;results)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Uses backsubstitution to solve the simultaneous equations.</TD>
</TR>
</TABLE>
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<P>

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<B>Method Detail</B></FONT></TD>
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<A NAME="getU()"><!-- --></A><H3>
getU</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/DenseMatrix.html">DenseMatrix</A> <B>getU</B>()</PRE>
<DL>
<DD>Get the U matrix.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>null if no matrix has been decomposed.</DL>
</DD>
</DL>
<HR>

<A NAME="getU(drasys.or.matrix.MatrixI)"><!-- --></A><H3>
getU</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A> <B>getU</B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)</PRE>
<DL>
<DD>Get the U matrix.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>null if no matrix has been decomposed.</DL>
</DD>
</DL>
<HR>

<A NAME="getV()"><!-- --></A><H3>
getV</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/DenseMatrix.html">DenseMatrix</A> <B>getV</B>()</PRE>
<DL>
<DD>Get the V matrix.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>null if no matrix has been decomposed.</DL>
</DD>
</DL>
<HR>

<A NAME="getV(drasys.or.matrix.MatrixI)"><!-- --></A><H3>
getV</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A> <B>getV</B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)</PRE>
<DL>
<DD>Get the V matrix.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>null if no matrix has been decomposed.</DL>
</DD>
</DL>
<HR>

<A NAME="getW()"><!-- --></A><H3>
getW</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/SparseMatrix.html">SparseMatrix</A> <B>getW</B>()</PRE>
<DL>
<DD>Get the W matrix.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>null if no matrix has been decomposed.</DL>
</DD>
</DL>
<HR>

<A NAME="getW(drasys.or.matrix.MatrixI)"><!-- --></A><H3>
getW</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A> <B>getW</B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)</PRE>
<DL>
<DD>Get the W matrix.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>null if no matrix has been decomposed.</DL>
</DD>
</DL>
<HR>

<A NAME="decompose(drasys.or.matrix.MatrixI)"><!-- --></A><H3>
decompose</H3>
<PRE>
public void <B>decompose</B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;matrix)
               throws <A HREF="../../../../drasys/or/linear/algebra/AlgebraException.html">AlgebraException</A></PRE>
<DL>
<DD>Decompose matrix A into U, W and V matrices.
Where: A[r][c] = U[r][c] * W[c][c] * transpose(V[c][c]) and W is a diagonal matrix of the singular values.<DD><DL>
<DT><B>Specified by: </B><DD><A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html#decompose(drasys.or.matrix.MatrixI)">decompose</A> in interface <A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html">DecompositionI</A></DL>
</DD>
</DL>
<HR>

<A NAME="solveEquations(drasys.or.matrix.VectorI)"><!-- --></A><H3>
solveEquations</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/DenseVector.html">DenseVector</A> <B>solveEquations</B>(<A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A>&nbsp;rightHandSides)
                           throws <A HREF="../../../../drasys/or/linear/algebra/AlgebraException.html">AlgebraException</A></PRE>
<DL>
<DD>Uses backsubstitution to solve the simultaneous equations.<DD><DL>
<DT><B>Specified by: </B><DD><A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html#solveEquations(drasys.or.matrix.VectorI)">solveEquations</A> in interface <A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html">DecompositionI</A></DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>the results.<DT><B>Throws:</B><DD><A HREF="../../../../drasys/or/linear/algebra/AlgebraError.html">AlgebraError</A> - if no matrix has been decomposed</DL>
</DD>
</DL>
<HR>

<A NAME="solveEquations(drasys.or.matrix.VectorI, drasys.or.matrix.VectorI)"><!-- --></A><H3>
solveEquations</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A> <B>solveEquations</B>(<A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A>&nbsp;rightHandSides,
                              <A HREF="../../../../drasys/or/matrix/VectorI.html">VectorI</A>&nbsp;results)
                       throws <A HREF="../../../../drasys/or/linear/algebra/AlgebraException.html">AlgebraException</A></PRE>
<DL>
<DD>Uses backsubstitution to solve the simultaneous equations.<DD><DL>
<DT><B>Specified by: </B><DD><A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html#solveEquations(drasys.or.matrix.VectorI, drasys.or.matrix.VectorI)">solveEquations</A> in interface <A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html">DecompositionI</A></DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>the results.<DT><B>Throws:</B><DD><A HREF="../../../../drasys/or/linear/algebra/AlgebraError.html">AlgebraError</A> - if no matrix has been decomposed</DL>
</DD>
</DL>
<HR>

<A NAME="computeInverse()"><!-- --></A><H3>
computeInverse</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/DenseMatrix.html">DenseMatrix</A> <B>computeInverse</B>()
                           throws <A HREF="../../../../drasys/or/linear/algebra/AlgebraException.html">AlgebraException</A></PRE>
<DL>
<DD>Computes the inverse of the decomposed matrix from the components.
Where: inverse(A) = V * diagonal(1/w[i][i]) * transpose(U).<DD><DL>
<DT><B>Specified by: </B><DD><A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html#computeInverse()">computeInverse</A> in interface <A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html">DecompositionI</A></DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>the results.<DT><B>Throws:</B><DD><A HREF="../../../../drasys/or/linear/algebra/AlgebraError.html">AlgebraError</A> - if no matrix has been decomposed</DL>
</DD>
</DL>
<HR>

<A NAME="computeInverse(drasys.or.matrix.MatrixI)"><!-- --></A><H3>
computeInverse</H3>
<PRE>
public <A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A> <B>computeInverse</B>(<A HREF="../../../../drasys/or/matrix/MatrixI.html">MatrixI</A>&nbsp;results)
                       throws <A HREF="../../../../drasys/or/linear/algebra/AlgebraException.html">AlgebraException</A></PRE>
<DL>
<DD>Computes the inverse of the decomposed matrix from the components.
Where: inverse(A) = V * diagonal(1/w[i][i]) * transpose(U).<DD><DL>
<DT><B>Specified by: </B><DD><A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html#computeInverse(drasys.or.matrix.MatrixI)">computeInverse</A> in interface <A HREF="../../../../drasys/or/linear/algebra/DecompositionI.html">DecompositionI</A></DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>the results.<DT><B>Throws:</B><DD><A HREF="../../../../drasys/or/linear/algebra/AlgebraError.html">AlgebraError</A> - if no matrix has been decomposed</DL>
</DD>
</DL>
<HR>

<A NAME="computeConditionNumber()"><!-- --></A><H3>
computeConditionNumber</H3>
<PRE>
public double <B>computeConditionNumber</B>()</PRE>
<DL>
<DD>Computes the condition number of the matrix.
The condition number is a measure of the singularity of the matrix.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>NaN is the matrix is singular.<DT><B>Throws:</B><DD><A HREF="../../../../drasys/or/linear/algebra/AlgebraError.html">AlgebraError</A> - if no matrix has been decomposed</DL>
</DD>
</DL>
<HR>

<A NAME="isIllConditioned()"><!-- --></A><H3>
isIllConditioned</H3>
<PRE>
public boolean <B>isIllConditioned</B>()</PRE>
<DL>
<DD>Returns true if the decomposed matrix is ill-conditioned.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Throws:</B><DD><A HREF="../../../../drasys/or/linear/algebra/AlgebraError.html">AlgebraError</A> - if no matrix has been decomposed</DL>
</DD>
</DL>
<HR>

<A NAME="isSingular()"><!-- --></A><H3>
isSingular</H3>
<PRE>
public boolean <B>isSingular</B>()</PRE>
<DL>
<DD>Returns true if the decomposed matrix is singular.<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Throws:</B><DD><A HREF="../../../../drasys/or/linear/algebra/AlgebraError.html">AlgebraError</A> - if no matrix has been decomposed</DL>
</DD>
</DL>
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